olymmath

HMMT November 2016 U30

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On the blackboard, Amy writes 2017 in base- aa to get 133201a133201_{a}. Betsy notices she can erase a digit from Amy's number and change the base to base-b such that the value of the the number remains the same. Catherine then notices she can erase a digit from Betsy's number and change the base to base- cc such that the value still remains the same. Compute, in decimal, a+b+ca+b+c.

Dataset text NuminaMath olympiads. Quoted with source.

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